INTRODUCTORY LECTURES
ON RINGS AND MODULES

CLASS NOTES

by John A. Beachy

These online notes are intended to help students who are working through the text. The notes will include some historical comments and background material, together with supplementary problems and solutions.
You will soon see that very little has been completed. I had hoped to finish the project by the end of 2001, but now I'm afraid it will have to wait a year, until after I return from a sabbatical leave.
Author's note from 2012: After that sabbatical leave, and one more, I'm now retired and plan to finally return to this writing project. But it is still several years from completion, even if I'm as optimistic as I was 12 years ago.
Please note that the files listed below are in .pdf format, suitable for viewing with Adobe Acrobat Reader.

Chapter 0: Introduction

0.1 Some history (a little about algebra; a little about Göttingen)
0.2 Vector spaces (some background for Chapter 2)
0.3 Abelian groups (more background for Chapter 2)

Chapter 1: Rings

1.0 Richard Dedekind
1.1 Basic definitions and examples: Problems | Solutions
1.2 Ring homomorphisms: Problems | Solutions
1.3 Localization of integral domains: Problems | Solutions
1.4 Unique factorization: Problems | Solutions
1.5 *Additional noncommutative examples:

Review problems | Solutions

Chapter 2: Modules

2.0 Emmy Noether
2.1 Basic definitions and examples: Problems | Solutions
2.2 Direct sums and products:
2.3 Semisimple modules:
2.4 Chain conditions:
2.5 Modules with finite length:
2.6 Tensor products:
2.7 Modules over principal ideal domains:

Review problems | Solutions

Chapter 3: Structure of Noncommutative Rings

3.0 Emil Artin
3.1 Prime and primitive ideals:
3.2 The Jacobson radical:
3.3 Semisimple Artinian rings:

Review problems | Solutions

Appendices, etc.

Some names
Biographies (in .html format, linked to The MacTutor History of Mathematics archive)
Timeline
Bibliography


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